Tracking Sigmoid Regression with Multicollinearity in Phase I: An Approach Incorporating Control Charts

Regression and quality control are two crucial techniques that data analysis employs in improving the decision-making process. We use the sigmoid function to model the connection between independent factors and the dependent variable in sigmoid regression. When there is a significant correlation among the independent variables in a regression model, multicollinearity a statistical phenomenon exists. Multicollinearity presents problems with higher uncertainty when estimating individual coefficients possibly making it harder to identify each variable's distinct contribution to the model. By suggesting a control chart specifically designed for the sigmoid regression model, this research presents a strategy to address the impact of influential observations using regression control charts, by making use of principal component regression class estimators. Principal component regression merges from the principal component analysis and linear regression methodologies, aiming to alleviate multicollinearity issues and enhances the stability of regression models. The performance of the model is evaluated using Pearson's residuals, Deviance residuals, and residuals. This strategy is proven to be useful in real world situations demonstrated through an application in the field of sleep wellness disorder. In conclusion, this study introduces a unique control chart to manage multicollinearity in sigmoid regression, providing a new perspective on the topic to spot differences in the underlying process by highlighting trends in the residuals.